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Statistical Variation and Strain-Rate Sensitivity of the Mechanical Properties of Individual PET Fib 5991-1552EN c20141030 [4]


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   Keysight Technologies
   Statistical Variation and Strain-Rate
   Sensitivity of the Mechanical Properties
   of Individual PET Fibers
   Application Note


                                                  Introduction                                 crystalline phases [3]. The final part of
                                                                                               the curve represents slippage between
                                                  Poly(ethylene terephthalate), or             microfibrils. It is important to note here
                                                  PET (also known as polyester), is a          that the changes in elastic properties
                                                  thermoplastic polymer used extensively       of a PET fiber during these different
                                                  as synthetic fiber. PET fibers are popular   deformation regimes were significant
                                                  because of their improved wrinkle            and have been measured previously
                                                  resistance, durability and high color        using continuous dynamic analysis
                                                  retention [1, 2]. Most characteristic        (CDA) [4].
                                                  physical properties of PET fibers are
                                                  attributed to the presence of benzene        During the deformation of the
                                                  rings, which also lead to high stiffness     amorphous regions, stress
                                                  of the polymer chains [1].                   concentration in the surface layer of
                                                                                               the fiber results in surface cracks and
                                                  The polymer chains in one individual         crazing in the PET fibers (horizontal
                                                  PET fiber can be distributed in              arrows in Figure 1). The propagation
                                                  crystalline, oriented semi-crystalline       of one or few of these cracks through
                                                  and non-crystalline (amorphous)              the sample is a stochastic process
                                                  regions [3]. A PET fiber consists of         depending on the distribution of
                                                  microfibrils aligned along the fiber axis.   crystalline and amorphous regions in
                                                  These microfibrils, in turn, consist of      the core of the fiber. Hence, it is not
                                                  crystalline and amorphous regions,           only important to characterize the
                                                  and connected to other microfibrils          mechanical properties of individual
                                                  by another kind of amorphous phase,          PET fibers, but also to understand
                                                  known as mesamorphous phase.                 the statistical variability in their
                                                  The different regions observed in the        response that can be extrapolated to
                                                  tensile stress-strain curve (Figure 1)       the underlying molecular structure and
                                                  can be explained by the deformation of       processing conditions.
Figure 1. Typical engineering stress-             the different microstructural regions
strain curve of an individual PET fiber. The                                                   Failure in materials is often a stochastic
                                                  mentioned above. During the initial
schematics outline the evolution in the                                                        process because of the distributions of
molecular structure of amorphous polymer          deformation, the amorphous regions
chains during different regimes of deformation.   within the microfibrils align themselves     defects and molecular structure, and it
                                                  in the similar orientation as the            has been successfully shown to follow
                                                  mesamorphous phase. The stress-strain        a Weibull statistical distribution of the
                                                  curve goes through another point of          form [5]
                                                  inflexion when the applied load starts to
                                                  strain the bonds in both amorphous and                                            (1)
where, Pf is the probability of failure of                                                       perform the Weibull analysis. The failure
a fiber at a stress less than or equal to                                                        probability, Pf, for each tensile strength
s, s0 is the characteristic strength, and                                                        was calculated as
is the Weibull modulus that describes
the variability of the failure strength. A                                                                                                    (4)
high Weibull modulus represents a more
uniform distribution, and hence better                                                           The data were then plotted and the
reliability. Rearrangement of the Weibull                                                        Weibull modulus was determined from
distribution (Eqn. 1) provides                                                                   Eqn. 2.

                                    (2)                                                          For determination of the strain-rate
                                                                                                 exponent, three tensile tests were
and hence the characteristic strength                                                            performed at strain-rates of 1 x 10 -1,
and Weibull modulus both can be              Figure 2. Engineering stress-strain curves          1 x 10 -2 and 1 x 10 -4 per second, each.
obtained from a plot of lnln(1/1-Pf)         obtained from quasi-static tensile tests on         The previous set of tests used for
                                             seven different PET fibers. Note the variation      determining Weibull modulus, were also
versus lns (known as Weibull plot). The
                                             in tensile strength values.
slope of the linear fit should produce                                                           used as the dataset for the strain-rate of
the Weibull modulus and the intercept                                                            1 x 10 -3 per second.
should produce the characteristic
                                              Keysight T150 



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